Section 3.4Solving Equations with

Variables on Both SidesObjectives:

Collect variables on one side of an equation

Collect like terms

When you play a game, you want to keep the teams equal. So when more people want to play, you add the same number of players to each team. This is the same concept of keeping both sides of an equation balanced.

Some equations have variables on both sides. To solve such equations, you will first collect the variable terms on the side with the greater variable coefficient.

EX: Solve the equations

1. 2.

3. 4.

13 5 2 8x x 6 22 3 31x x

64 12 6w w 9 9 4 10x x

Number of solutions

Linear equations can have one solution, many solutions, and no solutions.

Identity: an equation that is true for all values of the variable. The variable will cancel out and the numbers will equal. (many solutions)

No solution: an equation where the variable will cancel out and the numbers don’t equal

Solve the equation if possible

5. 6.

7. 8.

2 10 15 18 4 35

x x 4 5 4 20x x

9 12 9 3x x 14 5 5 205

x x

Solve the real-life problem

EX: A gym offers two packages for yearly membership. The first plan costs $50 to be a member. Then each visit to the gym is $5. The second plan costs $200 for a membership fee plus $2 per visit. Write and solve an equation to find how many times you must use the gym to have the same fee.

p. 15712 – 42 evens, 46, 50 – 52 all